(And this distinction is completely orthogonal to the question of whether same-sex couples get the right to be legally recognized as a couple or parents.)

I imagine that over time, any purported complete genealogy will make those distinctions but come to include information about both.

While both people in a same sex couple cannot claim parentage on the same child, one parent can. With multiple children each partner could claim parentage on one child, but not the other. This is not different than a 2nd marriage where each hetero partner can claim parentage on only 1 child.

In fact, in many instances you would not model "birth of couple X" but "person A and person B were married between years ...", "person C has father B and mother D".

Exactly because re-marriages and adultery, and children born out of wedlock has always been common (and known), so even if dealing with same sex couples is a reasonably new thing, dealing with children where linking their parentage to a specific couple is nothing new.

Of course, the practice of lying about family history is equally old, so in practice most genealogy becomes unreliable very quickly. In my own family tree, we have a child who in official registers is listed as having a mother we have lots of further data on, and the father is listed as a "Friedrich Denneche, travelling hat-maker from Bremen".

Problem is at the time (early 1800's I think), everyone had to register with local police when entering Oslo, and there is no record of any travelling hat-maker from Bremen. Nor did my dad find any records in Germany (though it's possible that there would be guild-records he did not find, he never got a chance to spend much time looking at German records) that matched.

His theory, which of course can't be proven, was that the real dad was the mothers brother-in-law. Especially as he took her in and later adopted the child and she lived with him and his wife (talk about awkward situation if my dads theory is true...). But at the time this happened, sexual relations between in-laws was legally considered incest in Norway, and it was a crime not to list the father on the birth certificate, and a crime to lie on it, so if the theory is true she was in a bind: she had to put down a father, but could not put down the real father without even worse problems, and could not put down someone who might find out and object. Inventing a person nobody would expect to be able to find would have been a safe way out.

Yes there is. Many countries have gender recognition laws which trans people to legally recognised as their true gender. A person can be genetically decended from two women.